measuring welfare with consumer surplus (chapter...

Gains From Trade Consumer Surplus Quantifying Welfare Effects Welfare in Competitive Equilibrium Market Demand

Measuring Welfare with Consumer Surplus(Chapter 14)


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Measuring Welfare

Q: How do we evaluate the performance of our institutions (e.g.markets)?

A: We need some social-welfare criterion.

Q: How can we. . .

Find a monetary measure of a consumer’s utility/happiness?

Evaluate a consumer’s willingness to pay for a unit of a good?

Evaluate whether or not a market maximizes welfare withoutgovernment intervention?

Quantify the effect of economic policy on consumers?

A: Use the concept of gains-from-trade


Gains From Trade

Example:

Your friend took Econ 100B last spring and no longer needthe text book. Values it at $10.

You need one before you take Econ 100A. You value it at$160.

It’s current allocation, with your friend, is inefficient.

If you trade, there is a social gain of $160 - $10 = $150

Who benefits from this gain? How is this $150 distributed?

That depends upon the terms of the trade.

Institutions are rules/regimes we have for determining howgoods are allocated.

Markets are particular kinds of institutions, in which buyersand sellers meet and agree on terms the terms of trade.

What the terms will be, what the outcome will be, dependsupon the features of the market.


Gains From Trade

Examples:

Suppose you had to pay to download iTunes, but once you did,you could buy as many songs as you like for $1.You have to pay a cover charge to get into a bar. Once you’rein, beers are $3.50 a pint.Costco sells cheap goods in bulk, but you have to pay amembership fee.

What is the most you would pay to enter these markets?

You would pay up to the dollar value of the gains-to-trade youwould enjoy once in the market.


Measuring Gains From Trade

Q: How can we put a dollar value on

a) the welfare gains resulting from a trade, or

b) the change in consumer welfare resulting from a price/policychange?

A:

a) Consumer and Producer Surplus are monetary approximationsof gains from trade for consumers & producers, respectively.(Benefits - Costs)

b) Our measure: welfare effect of change is change in consumer,producer surplus

c) Other ways to measure (e.g. compensating, equivalentvariation in book)


Willingness to Pay for 1 Unit

Q: How much would a consumer pay for a unit of a good?

A: Reservation Price = the maximum price that the consumeris willing to pay for a unit.

Example: suppose utility is quasilinear, i.e.

U(b, d) = v(b) + d ,

where b is the number of beers consumed and d is theamount of money (dollars) spend on other goods.

Successive reservation prices:

r1 = v(1)− v(0)

r2 = v(2)− v(1)...


Reservation Prices & Demand

Example: if r4 ≤ p ≤ r3, the consumer will demand 3 beers.

Reservation Price Curve for

02468

10

G li ( ll )

($) Res.Values

r6

r5

r4

r3

r2

r1

1 2 3 4 5 6

p

Beer

Reservation price

Assumption: the more you have already consumed, the lower thereservation price for the next good. (Downsloping demand)


Willingness to Pay for n Units

Q: How much is the consumer willing to pay for n beers?A: v(n). Why? Use reservation prices to show:

r1 + r2 + r3 = v(1)− v(0) + v(2)− v(1) + v(3)− v(2)

= v(3)− v(0) (assume v(0) = 0)

This is called gross benefit or gross gains from trade


02468

10

G li ( ll )

($) Res.Values

r6

r5

r4

r3

r2

r1

1 2 3 4 5 6

p

Beer

Reservation price


Expenditures

Q: How much does the consumer spend for n beers?A: Expenditure = pn


02468

10

G li ( ll )

($) Res.Values

r6

r5

r4

r3

r2

r1

1 2 3 4 5 6

p

Beer

Reservation price


Gains From Trade

(Net) Gains from Trade = gross benefit − expendituresin other words, net gain is v(n)− pn.


02468

10

G li ( ll )

($) Res.Values

r6

r5

r4

r3

r2

r1

1 2 3 4 5 6

p

Beer

Reservation price

This is the minimum amount of money the consumer would needto be paid to give up n units of the good.


Gains From Trade

With continuous units (if you can drink beer straight from the tap):

p

Price

Beer

Reservation-price curve


Consumer Surplus

Estimating the reservation-price curve is difficult.As an approximation, we replace the reservation-price curvewith the consumer’s ordinary demand curve.

p

Price

Beer

Demand curve


Consumer Surplus

Say what? Reservation-price curve 6= demand curve? Whynot?

Reservation-price curve describes sequential purchases ofsingle units

Demand curve describes willingness-to-pay for q unitspurchased simultaneously?

Q: What difference does it make? A: Income effects.

But. . . in our example, utility is quasilinear in income, so thereare no income effects & CS is an exact measure of gains fromtrade.


Quasilinear Utility & Income Effects: Huh?

How do we know that there are no income effects withquasilinear utility. . .

U(c , m) = v(c) + m

Clicker Vote: Which term shows us that there are no incomeeffects?

A) U(c , m)B) v(c)C) m linear, no DMU(m)

. . . and why does that matter?Decision to buy nth unit is the same regardless of whetheryou’ve already spent money on 0 or n − 1 units.


Consumer Surplus: Example

Suppose that the price of a beer is $4.25.

Q: How many beers will the consumer buy?A: 3Q: What is the consumer surplus?A: (10 + 8 + 6)− (3× 4.25) = $11.25


02468

10

G li ( ll )

($) Res.Values

1 2 3 4 5 6

p = 4.25

Beers demanded

Price


Consumer Surplus: Example

What if the price increases to $5.50?

Q: How many beers will the consumer buy?A: 3Q: What is the consumer surplus?A: (10 + 8 + 6)− (3× 5.50) = $7.50


02468

10

G li ( ll )

($) Res.Values

1 2 3 4 5 6

p = 5.50

Beers demanded

Price

Higher price means lower consumer surplus even though quantitydemanded may not change.


Change in Consumer Surplus

CS when price is p:

p

Price

Snuggly blankets

Demand curve

Consumer surplus

p’



CS when price is p′:

p

Price

Snuggly blankets

Demand curve

Consumer surplus

p’



Region A = change in CS due to higher price for all units consumedRegion B = change in CS due to reduction in consumption

A

pB

Price

Snuggly blankets

Demand curve

Consumer surplus

p’


Producer Surplus

Q: What about gains from trade for the producer?A: Changes in a firm’s welfare be measured in dollars as muchas for the consumerProducer Surplus = the area above the supply curve andunder the price line.

p

Price

Snuggly blankets

Supply curve= marginal cost

Producer surplus


Welfare in Equilibrium

Q: How can we measure the gain or loss caused by marketintervention/regulation?A: Use consumer and producer surplus: total surplus =CS + PS .Our benchmark will be competitive, free-market equilibrium

CS

p

Price

Snuggly blankets

Supply

Demand

PS

q

The competitive, free-market equilibrium and the gains from tradegenerated by it.


Welfare in Competitive Markets

Any regulation that causes the units from q1 to q0 to be nottraded destroys some of the gains from trade.

CS

QD, QS

Price

p

q0

PS

q1

Loss

This loss is the net cost of regulation.



Example: per unit tax of $t

CS

QD, QS

Price

q0

PS

q1

Loss

ps

pb

t TaxRevenue



Example: price floor pf

CS

QD, QS

Price

q0

PS

q1

Loss

pf



Example: price ceiling pc

QD, QS

Price

q0

PS

q1

Loss

pc

CS



Example: rationing (only q1 units allowed to be traded)

CS

QD, QS

Price

q0

PS

q1

Loss

ps

pb

Rationcoupon

Revenue


From Individual Demands to Market Demand

Let Di (p) be the demand function of person i and suppose that

D1(p) = max{20− p, 0}D2(p) = max{10− 2p, 0}

Cats

Price

D1(p)

Demand of Agent 1

20

20

Cats

Price

D2(p)

Demand of Agent 2

10

5


From Individual Demands to Market Demand

The market demand is the horizonal sum (for a given p) of allindividual demand:

D(p) =∑

i

Di (p)

= D1(p) + D2(p)

Cats

Price

D2(p)

Demand of Agent 2

10

5

D1(p)

20

20

kink

Market Demand

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